\[ A y(x) \left (a \sin ^2(y(x))+c\right )+y''(x) \left (a \sin ^2(y(x))+b\right )+a y'(x)^2 \sin (y(x)) \cos (y(x))=0 \] ✓ Mathematica : cpu = 29.0284 (sec), leaf count = 176
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}-\frac {\sqrt {2} \sqrt {\cos (2 K[1]) a-a-2 b}}{\sqrt {2 a A K[1]^2+4 A c K[1]^2-2 a A \sin (2 K[1]) K[1]+2 c_1-a A \cos (2 K[1])}}dK[1]\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sqrt {2} \sqrt {\cos (2 K[2]) a-a-2 b}}{\sqrt {2 a A K[2]^2+4 A c K[2]^2-2 a A \sin (2 K[2]) K[2]+2 c_1-a A \cos (2 K[2])}}dK[2]\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.463 (sec), leaf count = 138
\[\left \{-c_{2}-x +\int _{}^{y \left (x \right )}\frac {\sqrt {2}\, \left (a \left (\sin ^{2}\left (\textit {\_a} \right )\right )+b \right )}{\sqrt {-\left (-2 A \textit {\_a} a \cos \left (\textit {\_a} \right ) \sin \left (\textit {\_a} \right )+A a \left (\sin ^{2}\left (\textit {\_a} \right )\right )+\left (a +2 c \right ) A \,\textit {\_a}^{2}-2 c_{1}\right ) \left (a \left (\sin ^{2}\left (\textit {\_a} \right )\right )+b \right )}}d \textit {\_a} = 0, -c_{2}-x +\int _{}^{y \left (x \right )}-\frac {\sqrt {2}\, \left (a \left (\sin ^{2}\left (\textit {\_a} \right )\right )+b \right )}{\sqrt {-\left (-2 A \textit {\_a} a \cos \left (\textit {\_a} \right ) \sin \left (\textit {\_a} \right )+A a \left (\sin ^{2}\left (\textit {\_a} \right )\right )+\left (a +2 c \right ) A \,\textit {\_a}^{2}-2 c_{1}\right ) \left (a \left (\sin ^{2}\left (\textit {\_a} \right )\right )+b \right )}}d \textit {\_a} = 0\right \}\]